Exact output tracking for nonlinear time-varying systems

Solves the exact output tracking problem for nonlinear time-varying systems. The technique is even applicable in the nonminimum phase case, and uses an inverse trajectory for feedforward. The feedforward is coupled with a more conventional feedback control law for stable trajectory tracking. The inversion technique is new, even in the linear time-varying case, and relies on partitioning the linearized system dynamics into time-varying stable and unstable manifolds. This so-called dichotomic split is used to build time-varying filters which, in turn, are the basis of a contraction used to find the inverse trajectory. The method is local to the time-varying trajectory, but represents a significant advance relative to available tracking controllers which are restricted to time-invariant nonlinear systems, are much more difficult to compute than the scheme presented here, and track only asymptotically.<>